faktorisieren 16x^4-625y^4

Lösung

faktorisieren

16 x^{4} - 625 y^{4}

(4 x^{2} + 25 y^{2}) (2 x + 5 y) (2 x - 5 y)

Schritte zur Lösung

16 x^{4} - 625 y^{4}

16 x^{4} = (4 x^{2})^{2}

625 y^{4} = (25 y^{2})^{2}

= (4 x^{2})^{2} - (25 y^{2})^{2}

Wende Formel zur Differenz von zwei Quadraten an:

x^{2} - y^{2} = (x + y) (x - y)

(4 x^{2})^{2} - (25 y^{2})^{2} = (4 x^{2} + 25 y^{2}) (4 x^{2} - 25 y^{2})

= (4 x^{2} + 25 y^{2}) (4 x^{2} - 25 y^{2})

Faktorisiere

4 x^{2} - 25 y^{2} : (2 x + 5 y) (2 x - 5 y)

= (4 x^{2} + 25 y^{2}) (2 x + 5 y) (2 x - 5 y)

- 2 x \leq - 4

s im pl i f y - 4 - - 162 - 81 - - 72

f a c t or - 2 m^{2} + 19 m - 24

2 (x + \frac{3}{4})^{2} - 5 = 123

\frac{4}{3} x - \frac{2}{5} = \frac{7}{5} x - \frac{1}{10}